{"paper_id":"31b8494a-eae2-4d95-a49d-3ebdf6831ddd","body_text":"Developing epidemiological\npreparedness for a plant disease\ninvasion: modelling citrus\nhuánglóngbìng in the European\nUnion\nJohn Ellis1,2†, Elena Lázaro 3,4†, Beatriz Duarte 5, T omás Magalhães5,\nAmílcar Duarte5, Jacinto Benhadi-Marín 6, José Alberto Pereira 6, Antonio\nVicent3, Stephen Parnell7,8 , Nik J. Cunniffe 1∗\n1Department of Plant Sciences, University of Cambridge, Cambridge, United Kingdom. 2School of Pub-\nlic Health, Imperial College London, White City Campus, London, United Kingdom. 3Institut Valencià\nd’Investigacions Agràries (IVIA), Centre de Protecció Vegetal i Biotecnologia, Moncada, Valencia, Spain.\n4Departament d’Estadística i Investigació Operativa, Universitat de València, Burjassot, Valencia, Spain.\n5MED – Mediterranean Institute for Agriculture, Environment and Development & CHANGE – Global\nChange and Sustainability Institute, Universidade do Algarve, Campus Gambelas, 8005-139 Faro, Portu-\ngal. 6CIMO, SusTEC, Instituto Politécnico de Bragança. Campus de Santa Apolónia, 5300-253 Bragança,\nPortugal. 7 Warwick Crop Centre, University of Warwick, Wellesbourne Campus, Warwick, United King-\ndom. 8 The Zeeman Institute for Systems Biology & Infectious Disease Epidemiology Research, University\nof Warwick, Coventry, United Kingdom.\n† Current address.\n∗Corresponding author njc1001@cam.ac.uk.\nKey words: Candidatus Liberibacter, citrus greening, Diaphorina citri\nKuwayama, early detection surveillance, HLB, psyllid, stochastic epi-\ndemic model, Trioza erytreae Del Guercio (1918)\nAbstract\nHuánglóngbìng (HLB; citrus greening) is the most damaging disease\nof citrus worldwide. While citrus production in the USA and Brazil\nhave been affected for decades, HLB has not been detected in the\nEuropean Union (EU). However, psyllid vectors have already invaded\nand spread in Portugal and Spain, and in 2023 the psyllid species\nknown to vector HLB in the Americas was first reported within the\n1\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\nEU. We develop a landscape-scale, epidemiological model, account-\ning for heterogeneous citrus cultivation and vector dispersal, as well\nas climate and disease management. We use our model to predict\nHLB dynamics following introduction into high-density citrus areas in\nSpain, assessing detection and control strategies. Even with signifi-\ncant visual surveillance, we predict any epidemic will be widespread\non first detection, with eradication unlikely. Introducing increased in-\nspection and roguing following first detection, particularly if coupled\nwith intensive insecticide use, could potentially sustain citrus produc-\ntion for some time. However, this may require chemical application\nrates that are not permissible in the EU. Disease management strate-\ngies targeting asymptomatic infection will likely lead to more success-\nful outcomes. Our work highlights modelling as a key component of\ndeveloping epidemiological preparedness for a pathogen invasion that\nis, at least somewhat, predictable in advance.\nIntroduction\nConsequences of plant disease epidemics threaten ecosystem ser-\nvices (Boyd et al., 2013) and food security (Strange and Scott, 2005).\nEmerging pathogens, which cause disease in new locations or on new\nplant host species, can be particularly damaging (Ristaino et al., 2021).\nHowever, emerging epidemics are well documented (Rosace et al.,\n2023; Jeger et al., 2023; Fielder et al., 2024), and invasion rates are\nincreasing (Bebber et al., 2014). Drivers include changes to farming\npractices and land use (Anderson et al., 2004), climate change (Singh\net al., 2023), and increased travel and trade (Brasier, 2008).\nRising invasion rates have focused attention on how emerging epi-\ndemics can be detected and controlled (Cunniffe and Gilligan, 2020).\nIt is particularly important to anticipate and be able to react quickly to\ninvasions, since this gives control the best chance of success (Fraser\net al., 2004). But effective detection and control strategies can be\n2\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\nhard to devise for invading pathogens because epidemiology in new\nlocations is inadequately characterised (Thompson et al., 2018). Math-\nematical modelling can play a key role. Models offer a rational basis to\nintegrate what is known with what is not known to design surveillance\n(Parnell et al., 2017) and to determine when, where and how to con-\ntrol disease (Cunniffe et al., 2015a). However, modelling of emerging\nplant pathogens has very often been done retrospectively (e.g., Cun-\nniffe et al. (2016), Radici et al. (2024)).\nHere we focus on modelling in advance of an invasion that is, at\nleast somewhat, predictable. We use citrus greening (aka huánglóng-\nbìng, HLB) in the European Union (EU) as a timely and socioeconomi-\ncally important case study. Worldwide, citrus is an important crop, and\nHLB its most devastating disease (Gottwald, 2010). HLB has been\nreported in over 60 countries (Zhang et al., 2023), and impacts on\nthe citrus industries of Brazil and the USA are significant. For exam-\nple, since 2005 citrus production in Florida has decreased by 80% ,\nwhereas in Brazil over 64 million trees have been removed in São\nPaulo state (Graham et al., 2024). However, HLB has not been re-\nported in the EU, and citrus production in the Mediterranean Basin\nremains unaffected (Wang, 2020), although recent discoveries of a\nhigh-profile vector species in Israel (EPPO, 2022) then in the EU itself\nin Cyprus (EPPO, 2023) are concerning.\nHLB is associated with three non-cultivable phloem-restricted bac-\nteria: Candidatus Liberibacter asiaticus (CLas), Ca L. africanus (CLaf)\nand Ca L. americanus (CLam) (Bové, 2006). HLB is primarily transmit-\nted by two insect vectors, the Asian citrus psyllid (ACP), Diaphorina\ncitri Kuwayama (Hemiptera: Psyllidae), and the African citrus psyllid\n(AfCP), Trioza erytreaeDel Guercio (1918) (Hemiptera: Triozidae). ACP\nhas been found in Asia, North America, South America, and a few lo-\ncations in Africa. There have also been recent detections of ACP in\nIsrael (EPPO, 2022) and Cyprus (EPPO, 2023). AfCP has been found in\nmany countries in Africa and the Middle East, and was detected in Eu-\nrope in 2014 (Perez-Otero et al., 2015), with subsequent spread over\n3\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\nlarge areas of northwestern Spain and western Portugal (EFSA et al.,\n2019b). It has been shown experimentally that both ACP and AfCP\nvector CLas (Reynaud et al., 2022), the most aggressive of the three\nbacteria causing HLB (Bové, 2006).\nBoth the recent detections of ACP in Israel and Cyprus and the es-\ntablished presence of AfCP in Spain and Portugal are concerning, since\neither vector could facilitate HLB transmission were a pathogen to be\nintroduced (Cocuzza et al., 2017). Although contingency plans for the\narrival of HLB in Spain and Portugal exist (DGAV, 2021; BOE, 2023),\nand have been tested in formal simulation exercises (Aragón et al.,\n2022), designing an effective response is challenging. Management\ninterventions that have been used somewhat successfully in other ar-\neas might not translate to the EU, since important epidemiological as-\npects are different. For example, there are differences in how commer-\ncial and non-commercial citrus are distributed (Moreira et al., 2019), in\nclimatic drivers of vector population dynamics (Cocuzza et al., 2017),\nand in regulations dictating which pesticides can be applied and how\noften (Urbaneja et al., 2020). Each of these factors has knock-on ef-\nfects upon outbreak management. This is precisely when modelling is\nmost useful.\nHere we show how modelling can contribute to developing epi-\ndemiological preparedness for a plant pathogen. We have developed\na flexible and transferable stochastic landscape-scale model, which\naccounts for heterogeneity in the citrus host landscape, spatial spread\nof a vector (including effects of climate and disease management on\nits population dynamics), and the concomitant spread of HLB. We fo-\ncus here on the Iberian Peninsula – Spain and Portugal – driven by\nthe availability of citrus density data, and the status of Spain as the\nlargest citrus producer in the EU (Schimmenti et al., 2013). Data from\nthe spread of AfCP in Spain and Portugal to date is used to parame-\nterise psyllid dispersal in our model. However, the fitted model can be\napplied to any EU region, assuming climatic and citrus host data were\navailable.\n4\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\nWhile our model must track spread across large areas of Spain and\nPortugal when fitting psyllid dispersal parameters, our major focus\nis to assess and compare surveillance and control strategies before\nand during the early stage of any epidemic. We do not aim to pre-\ndict precisely where in the EU the pathogen will enter, and so do\nnot attempt to model relative risks of primary infection for different\nregions (Douma et al., 2016). Instead, we concentrate on the situa-\ntion as faced directly before and after an initial incursion, restricting\nour attention to two representative 50km × 50km regions in Spain\nwithin which commercial citrus is grown at high-density and where\nHLB and/or AfCP and/or both could be introduced.\nWe demonstrate how an uncontrolled outbreak might spread if HLB\nentered, and how the speed of invasion would depend on whether\nAfCP was already locally widespread. We then investigate early de-\ntection surveillance, testing how the size of any epidemic at the point\nof first detection responds to the frequency and intensity of surveys.\nFinally, we assess the effectiveness of strategies for disease control,\nshowing how relative efficacy can be quantified. By comparing results\nfor two regions, we test the robustness of our conclusions.\nMethods\nModelling spread of pathogen and vector\nCitrus host distribution\nCommercial and residential/municipal (henceforth \"residential\") citrus\nwere mapped across Spain and Portugal, and rasterised at1km ×1km\nresolution (Fig. 1(B); see also S1 Supporting Methods). For cell, citrus\ndensities (hc\nandhr\n) were converted into pairs of integer-valued num-\nbers of “host units” (0 ≤Hc\n≤100 and0 ≤Hr\n≤1,000) for compatibil-\nity with our epidemiological model. We used different discretisations\nfor commercial and residential citrus to allow our model to properly\n5\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\ncapture within-cell epidemiological dynamics, since within-cell densi-\nties are rather different (Fig. 1(C)), largely because commercial trees\nare typically planted in rows of hundreds/thousands of trees in close\nproximity. By separating commercial and residential citrus, our model\ncan capture systematic differences in disease detection and control\nbetween settings.\nBacterium and vector\nWe focus on theCLas bacterium as it is the most damaging, as well as\nthe most likely to be introduced due to large and ongoing epidemics\nworldwide (Gottwald, 2010). We focus on AfCP as the vector, moti-\nvated by the availability of psyllid spread data from the recent inva-\nsion of northwestern Spain and Portugal (Cocuzza et al., 2017), and\nconcomitant risk of spread of AfCP to regions of the Iberian Peninsula\nwith commercial citriculture.\nDisease and vector status within each cell\nOur model tracks the HLB status of each citrus host unit in each cell,\nfor both residential and commercial citrus. We distinguish: (S)usceptible,\n(E )xposed, (C )ryptic, ()nfected and (R)emoved (Fig. 2). Susceptible\nhost units are uninfected. Exposed host units are latently infected,\ni.e., not yet infectious. Cryptic host units are infectious but not yet\nsymptomatic (Craig et al., 2018). Infected host units are infectious\nand symptomatic. Removed host units have been rogued (i.e., re-\nmoved following detection to slow or stop the spread of disease). We\ndo not account for other citrus demography, e.g., planting or disease-\ninduced/natural death.\nEpidemiological transitions of host units – and all other events in\nthe Matlab implementation of our stochastic model – are simulated\nusing Gillespie’s algorithm (Keeling and Rohani, 2008). Transitions\nfrom E →C and C →occur at fixed rates μand ν, respectively, with\n6\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\nTotal citrus density Climate suitability for AfCP \nCitrus density within Region A: Valencian Community region.  \n50 km \n50 km \nTotal Residential \n= + \nCommercial \nA B C \nD \n200 km 200 km \nCitrus density within Region B: Andalusia region. \n50 km \n50 km \nTotal Residential \n= + \nCommercial \nE \nA \nB \nCitrus density Citrus density \nCitrus density \nFrequency \nCitrus density distribution \nFigure 1: Climate suitability and citrus density across the Iberian\npeninsula. (A) AfCP climate suitability (see S1 Supporting Methods). (B) T otal\ncitrus density (residential + commercial) for each 1 km × 1 km cell, with our two\n50 km × 50 km focal regions labelled. (C) Frequency distributions of (non-zero)\nresidential and commercial citrus densities in each cell. (D) Residential,\ncommercial and total citrus density maps (Region A), within the Valencian\nCommunity region, on the east coast of Spain. (E) Residential, commercial and\ntotal citrus density maps (Region B), within Andalusia, in southern Spain.\naverage latent period of 1 year, and average incubation period (i.e.,\nto detectable symptoms) of 1.25years (Parry et al., 2014) (T able 1).\nThe rate at which host units transition from S →E , λ, is complex, and\n7\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\nE\nExposed host\nX\nVector is absent\nZ\nInfested by \nvector\nS\nSusceptible \nhost\nI\nInfected host\n𝛾\n𝜆\nDispersal of the pathogen by the vector\nInfection rate from within \ncell, local and long-\ndistance dispersal\nC\nCryptic host\nInfestation rate via local \nand long-distance \ndispersal (from other \ncells)\nY\nExposed to \nvector\nν\nη\nμ R\nRemoved host\nRemoval only starts \nwhen the disease has \nbeen detected.\nω\nFigure 2: Model of vector (AfCP) and pathogen (CLas) in each 1km × 1km\ncell. We track each cell’s vector infestation status, for each class of citrus\n(residential/commercial), distinguishing: free of vector, X, exposed (psyllid is\npresent, but has not yet fully colonised the cell),Y, and infested, Z. We also track\nthe disease status of citrus within each cell, quantifying local densities of infection\nby tracking the number of host units in each epidemiological class in each cell,\nagain distinguishing residential from commercial citrus. Epidemiological classes:\nsusceptible (free from HLB),S; exposed (latently infected),E ; cryptic (infectious\nbut not symptomatic), C ; infected (infectious and symptomatic), ; and removed,R\n(controlled by roguing). The rate from X →Y, γ, is the combination of local and\nlong-distance dispersal of the vector (, Eqns. 2-3 and Ω, Eqn. 4). The rate from\nS →E , λ, is the equivalent combination for infection (Λ, Eqns. 5-6, and Ω, Eqn. 4).\ndepends on psyllid dispersal and the infection status of citrus within\nthe cell of interest and elsewhere, as described below. The transition\nfrom→R occurs at rateω, and depends on the detection and control\nstrategy adopted, since it corresponds to roguing.\nAfCP is currently only present in northwestern Spain and western\nPortugal, and so we model whether each cell’s citrus is infested by\nthe psyllid. The model tracks whether cells are colonised by popu-\nlations of psyllids that are sufficiently well-established for dispersal\nelsewhere, distinguishing infestation statuses of residential and com-\nmercial citrus. For each class of citrus, in each cell, there are three\n8\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\npossibilities: vector absent ( X), exposed ( Y), and infested ( Z). Ex-\nposed corresponds to a recently arrived vector population which is\nnot yet capable of further dispersal. The rate of the X → Y transi-\ntion,γ, is complex, and is described below. We assume the rate of the\nY →Ztransition isη=1yr−1, corresponding to an average of one year\nfor psyllid populations to fully colonise cells (see also S1 Supporting\nMethods).\nFollowing colonisation, relative psyllid population densities in cell,\nVr\nand Vc\n, depend on local citrus densities and environmental condi-\ntions\nVr\n=hr\nZr\n, and Vc\n=hc\nm Zc\n, (1)\nwhere hr\nand hc\nare proportions of residential/commercial citrus (0 ≤\nhr\n,hc\n≤1) andis the climate suitability for psyllids (0 ≤≤1; see\nalso S1 Supporting Methods). For commercial citrus, the effect of pest\nmanagement, m is also included (0 ≤ m ≤ 1; see also S1 Support-\ning Methods, and note our mapping procedure allows us to account\nfor a lack of management in abandoned and/or organic orchards). In\nEqn. 1 the infestation status (i.e., Zr\nor Zc\n) acts as an indicator func-\ntion to ensure psyllid densities are only non-zero when the cell is fully\ncolonised.\nInteractions between cells\nScales of dispersal. We distinguish two scales of dispersal. The\nlocal dispersal kernel, Koc\nj, reflects psyllid movement between an in-\ndividual cell, , and one of its near neighbours, j. For this we use\nan exponential kernel as fitted to spread of ACP in the United States\nby Nguyen et al. (2023). However, psyllids can occasionally travel\nmuch further, due to extreme wind (Antolinez et al., 2021) or human\ntransportation (Nunes et al., 2023). We capture these relatively infre-\nquent long-distance dispersals using t-distribution kernel as fitted to\nthe AfCP invasion in Portugal by Benhadi-Marín et al. (2020). Mathe-\nmatical details are in S1 Supporting Methods.\n9\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\nDispersal of psyllids. Local dispersal of psyllids (AfCP) occurs from\npopulations which have colonised neighbouring cells, with local forces\nof infestation on cell \nr\n=1(Hr\n>0,Xr\n=1)δ(1 −ζ)\nX\nj\nKoc\nj(Vr\nj +Vc\nj ), (2)\nand\nc\n=1(Hc\n>0,Xc\n=1)δ(1 −ζ)m \nX\nj\nKoc\nj(Vr\nj +Vc\nj ), (3)\nwhereHr\n,Hc\n>0 andXr\n,Xc\n=1 ensure only cells containing citrus but\ncurrently psyllid-free can become infested, Vr\nj and Vc\nj are densities\nof (established) psyllid populations in residential/commercial citrus in\ncellj,Koc\njis the local dispersal kernel,δis the rate of psyllid dispersal,\nandζis the proportion of long-distance dispersals. For both residential\nand commercial citrus, forces of infestation include , representing\nclimatic effects. For commercial citrus,m is also included in Eqn. (3),\nrepresenting reduced establishment probability due to pest manage-\nment.\nOur model implements the “particle-emission” formulation of long-\ndistance dispersal (Meentemeyer et al., 2011). Rates of long-distance\ndispersal from cellare\nΩr\n=δζVr\n and Ωc\n=δζVc\n, (4)\nwhere δis the dispersal rate, ζis the proportion of long-distance dis-\npersals, and Vr\nand Vc\nare densities of psyllid populations in residen-\ntial/commercial citrus in cell . Whenever a long-distance dispersal\nevent is sampled by our Gillespie algorithm, the angle of dispersal is\ndrawn uniformly on [0,2π), and a distance sampled from the long-\ndistance dispersal kernel. If the corresponding destination cell,j, con-\ntains citrus, the type of citrus challenged (residential or commercial)\nis randomly chosen according to the proportion of each type. The\nprobability the vector will infest is given byj for residential citrus, or\n10\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\njm j for commercial citrus. If cell jdoes not contain citrus, the vector\nsimply fails to disperse.\nSpread of infection. Infection rates are closely coupled to psyllid\ndispersal. However, since our model captures HLB dynamics within in-\ndividual cells, within- and between-cell infection must be distinguished.\nThe rate of local infection of susceptible host units in residential citrus\nin cell(i.e., the component of the rate of theS →E transition in cell\ncorresponding to within-cell and nearby sources of infection) is\nΛr\n=1(Hr\n>0)β\nSr\n\nHr\n\n\nρ\n€\nJr\nVr\n+Jc\nVc\n\nŠ\n+ (1 −ρ)\nX\nj,j̸=\nKoc\nj\n€\nJr\njVr\nj +Jc\njVc\nj\nŠ\n\n, (5)\nand for commercial host units is\nΛc\n=1(Hc\n>0)β\nSc\n\nHc\n\n\nρ\n€\nJr\nVr\n+Jc\nVc\n\nŠ\n+ (1 −ρ)\nX\nj,j̸=\nKoc\nj\n€\nJr\njVr\nj +Jc\njVc\nj\nŠ\n\n. (6)\nIn Eqns. 5 and 6, βis the infection rate, Sc\n/Hc\nand Sr\n/Hr\nare propor-\ntions of uninfected commercial/residential host units in cell , ρis the\nproportion of within-cell transmission, and Jc\nj and Jr\nj are proportions of\ninfectious commercial/residential citrus in cellj, i.e.,\nJr\nj = (r\nj +C r\nj)/Hr\nj, and Jc\nj = (c\nj +C c\nj)/Hc\nj. (7)\nLong-distance transmission of HLB is a consequence of psyllid move-\nment. Whenever long-distance psyllid dispersal occurs from residen-\ntial citrus in cell , the probability the recipient cell ( j) gains a sin-\ngle HLB exposed host unit is given by Jr\n(Sr\nj/Hr\nj) or Jr\n(Sc\nj/Hc\nj), depend-\ning on whether the long-distance dispersal challenges residential or\ncommercial citrus. Analogous probabilities involvingJc\nset the chance\nof infection from long-distance dispersal from cell originating within\ncommercial citrus. There is no requirement for a vector population to\n11\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\nT able 1: Model parameters, descriptions, values and sources. Model fitting is\ndescribed in overview in the main text, with further details in S1 Supporting\nMethods.\nParameter Estimate and source\nδ Psyllid dispersal rate 1,600d−1 Fitted (see text)\nζ Proportion of long-distance dispersal 0.001 Fitted (see text)\nαoc Local dispersal scale 1.96km Nguyen et al. (2023)\nαd Long-distance dispersal scale 130km Benhadi-Marín et al. (2020)\nm Vector reduction in commercial citrus 0.9 Qureshi et al. (2014)\nη Rate of vector establishment 1/365d−1 Assumed/fitted (see text)\nβ Infection rate 10d−1 Fitted (see text)\nρ Proportion of within cell infection 0.7 Fitted (see text)\nμ Exposed to cryptic transition rate 1/365d−1 Parry et al. (2014)\nν Cryptic to symptomatic transition rate 5/365d−1 Parry et al. (2014)\nω Roguing rate 0 No control by default\nestablish in the recipient location for transmission of the bacterium,\nand so parameters for climate and pest management are not included\nin these probabilities. However, of course, infection will not be able to\nspread onwards from any infected cell until a psyllid population does\ncolonise locally.\nParameterisation\nWe fix values of five parameters in our model from the literature (T a-\nble 1): αoc(scale of local psyllid dispersal);αd(scale of long-distance\npsyllid dispersal); m (effect of insecticide sprays on psyllid popula-\ntions); μ(rate at which exposed hosts become cryptic); and ν(rate\nat which cryptic hosts become symptomatic). The rate of roguing, ω,\ndepends on the control strategy, and in model runs without disease\ncontrol we assumeω=0.\nHowever, five remaining parameters are fitted to data (S1 Support-\ning Methods). These are: δ(dispersal rate of psyllids);ζ(proportion of\nlong-distance psyllid dispersal);η(rate at which psyllids fully colonise\na cell following first infestation); β(pathogen transmission rate); and\nρ(rate of within-cell relative to between-cell infection). Parameters δ\nand ζare fitted to AfCP presence data from surveys in Portugal and\n12\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\nSpain up to 2021 (Benhadi-Marín et al., 2022), contingent on an as-\nsumed value of η. T o fit parameters βand ρ, we calibrated results\nour model against a previous model of the spread of HLB ( CLas vec-\ntored by ACP) in Florida (Mastin et al., 2020). Full details are in S1\nSupporting Methods.\nModelling detection and control\nEarly detection\nBefore first detection, we model regular inspections everyΔ(“inspec-\ntion interval”) years, withc% andr% of cells containing commercial\nand residential citrus, respectively, across our 50km × 50km region,\nrandomly selected on each round of inspection. Selection is weighted\nby within-cell citrus density. Within each selected cell, at any inspec-\ntion, nh host units are selected at random (if the cell has fewer than\nnh host units of the prescribed type, all are inspected). Disease is de-\ntected with probabilityp on each symptomatic (i.e., class ) host unit.\nThe first inspection is at a random time on [0,Δ), where0 is the time\nof first introduction.\nControl\nFollowing first detection, we assume inspection significantly intensi-\nfies, occurring according to the roguing interval, ΔR (generally with\nΔR < Δ). This detection regime applies across the region, and so we\nassume the entire 50km × 50km area corresponds to the Infested\nZone under Regulation (EU) 2016/2031 (European Union, 2016). We\nassume the increased threat of disease encourages most stakehold-\ners to participate in enhanced detection and control. However, since\nsome growers will not cooperate, we introduce a compliance parame-\nter, c, and assume only a proportion c of growers comply. The set of\nnon-complying growers remains fixed for each simulation. We assume\nthat detection and control does not occur within the cells containing\n13\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\nnon-compliant growers. However, we assume all host units in all com-\nplying cells are inspected on each roguing interval.\nDetection of symptomatic host unit(s) triggers roguing (i.e., re-\nmoval of host). Following detection, which as for early detection\noccurs with probability p for symptomatic host units, each detected\nhost unit is (immediately) removed with probability q. With probabil-\nity 1 −q a host unit will not be removed, although of course it may\nbe re-detected and removed later. The roguing probability, q, there-\nfore acts as a proxy for any delays in control and/or imperfect man-\nagement by growers or plant health authorities. We also allow for\ncommercial growers applying extra pest management following first\ndetection. This reduces the vector population by a further factor m ∗,\nover-and-above the reduction by m caused by “standard” pest man-\nagement. We model this by assuming m is increased by (1 −m )m ∗\nacross the entire region of interest immediately after first detection,\nand that this decreases vector populations in commercial citrus (while\naccounting for abandoned/organic citrus, and only for the subset of\ngrowers who comply).\nParameterisation\nSince CLas is an EU priority pest (European Union, 2016, 2019), an-\nnual surveys are mandatory, and so inspection is assumed once per\nyear (Δ=1yr). We assume by default (see also T able 2) c =1% of\ncells with commercial citrus are (randomly) surveyed each year, and\nwithin each cell nh =5 (commercial) host units are inspected. How-\never, by default residential citrus is not inspected (r =0%), reflecting\nthe difficulty of surveillance in private gardens and other residential\nsettings (Cocuzza et al., 2017). We assume the probability of (visual)\ndetection of symptomatic hosts is p =0.5(Mastin et al., 2020).\nAfter detection of the pathogen anywhere within the region, our\nbaseline is that the default compliance rate of commercial growers\nis 90% (i.e., c = 0.9). For those growers who comply, the roguing\n14\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\nT able 2: Default parameters for detection and control strategies. There is\ninitially an early detection phase, but following detection anywhere across the\nregion, the strategy switches to include more intensive surveillance and active\ndisease control (details in text).\nParameter Value\nEarly detection\nΔ Inspection interval 1yr\nc Percentage of commercial cells surveyed 1%\nr Percentage of residential cells surveyed 0%\nnh Number of host units sampled per surveyed cell 5\np Probability of detection of symptomatic host units 0.5\nControl following first detection\nΔR Roguing interval 0.5yr\nc Percentage of commercial cells surveyed 100%\nr Percentage of residential cells surveyed 0%\nnh Number of host units sampled per surveyed cell 100\np Probability of detection of symptomatic host units 0.5\nc Proportion of stakeholders who comply with control 0.9\nq Roguing probability 0.9\nm ∗ Effectiveness of additional spraying by commercial growers 0\ninterval is ΔR = 0.5 (i.e., detection/control every 6 months) and all\ncommercial citrus units are inspected within all cells ( nh =100, c =\n100%). The roguing probability is q = 0.9. However, we assume\nresidential citrus remains uninspected ( c\nR = 0%); because of this,\nby default we assume no roguing is done for residential citrus. We\nalso assume there is no additional pest management introduced by\ncommercial growers (i.e., m ∗ =0). However, our sensitivity analyses\nallow consequences of these choices to be tested.\nResults\nDisease spread without control\nWe initially focus on Region A (Fig. 1(D)), in the Valencian Commu-\nnity region (eastern Spain), one of the main citrus growing regions in\nthe EU. If both the vector and HLB are introduced simultaneously into\na single cell, HLB spreads rapidly (Fig. 3 and S3 Supporting Videos\n15\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\n0\n0.2\n0.4\n0.6\n0.8\n1\n0\n0.2\n0.4\n0.6\n0.8\n1\n0\n0.2\n0.4\n0.6\n0.8\n1\n0\n0.2\n0.4\n0.6\n0.8\n1\n0\n0.2\n0.4\n0.6\n0.8\n1\n0 2 4 6 8 10 12 14 16 18 20\n0\n0.2\n0.4\n0.6\n0.8\n1\nFigure 3: Spread of the pathogen in a single simulation in Region A\n(Valencia). Both vector and pathogen are introduced simultaneously att=0 into\na single1km × 1km cell (asterisked in panel (A)). A single host unit of commercial\ncitrus is moved fromS →E , and the psyllid status of commercial citrus in that cell\nset to Y. (A)-(E) Maps showing the density of infected citrus host units (E +C +)\nwithin each cell at different times after introduction; see also S3 Supporting Videos\n(Video 2). (F) Disease progress curve showing proportions of citrus over the entire\nregion in each epidemiological compartment, (S)usceptible, (E)xposed, (C)ryptic\nand (I)nfected (no host units are (R)emoved, since disease control by roguing was\nnot done in the underpinning simulation).\n16\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\n(Video 2)), although spread of the vector is – of course – even faster\n(S2 Supporting Results, Fig. S10, and S3 Supporting Videos, Video\n1). Several cells near to the point of initial introduction and two cells\nwhich are further away become HLB positive within the first year in\nthis single simulation (Fig. 3(A)). Almost all cells with citrus have at\nleast one infected citrus host unit by year10 (Fig. 3(D)), and within20\nyears almost all susceptible citrus across the entire region is infected\n(compare Fig. 3(E) with Fig. 1(D)).\nAlthough individual simulations are easy to visualise, only ensem-\nbles of multiple simulations capture the range of possibilities from our\nstochastic model. Although the vector spreads rapidly, and it does not\ntake long for an initial vector population to become widely dispersed,\nif the vector is already widespread at the time of pathogen entry, HLB\ninvasion is faster, since spread can begin immediately (compare Figs.\n4(A) and 4(B)). Prediction intervals are wider when the vector must\nalso spread, since the variability in the spread of the vector has a\nknock-on effect upon HLB. This is particularly pronounced when the\nvector is (randomly) introduced into a cell with low density citrus.\nHenceforth, we focus exclusively on the case in which the vector\nis already widespread in the region of interest. However, in all sub-\nsequent simulations, the initial location of CLas infection is selected\nat random (weighted by commercial citrus density, assuming that the\npathogen is introduced on planting material, and that higher density\ncommercial operations plant larger amounts more frequently).\nEarly detection surveillance\nWe test early detection surveillance by varying the proportion of com-\nmercial cells inspected on each survey (c), and the interval between\nsuccessive surveys (Δ), considering three indicative probabilities of\ndetection: p =0.2,0.5and0.8. We vary c from0.5% (9 cells across\nRegion A), to 5% (83 cells). We vary the inspection interval ( Δ) from\nonce every3months to once every2 years. The number of host units\n17\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\n(A) Vector already widespread (B) Simultaneous introduction\nFigure 4: Effect of prior invasion by the vector on pathogen spread in\nRegion A (Valencia). The percentage of cells infested by the vector (red), with at\nleast one infected unit of citrus (yellow) and the percentage of all citrus infected\n(blue), when the vector is already widespread throughout the region of interest\n(Panel (A)) versus when the vector and pathogen are introduced simultaneously\n(Panel (B)). In all cases the pathogen is introduced into the same cell att=0; for\nthe simulations shown in Panel (B), the cell initially infested by the vector is chosen\nat random from all cells containing commercial citrus. Shaded regions show 95%\nprediction intervals from an ensemble of200 simulation results.\nof citrus to inspect per cell is fixed at the default value nh =5 (this is\nrelaxed in S2 Supporting Results, Fig. S11).\nWe summarise performance via the time until first detection and\nproportion of citrus then infected (Fig. 5). Unsurprisingly, effective\nearly detection is conditioned on inspecting as many cells as possi-\nble, as often as possible (Figs. 5(A) and (D)). However, we note the\nvariability in both time of first detection (Figs. 5(B) and 5(E)) and\n(particularly) the proportion of citrus infected (Figs. 5(C) and 5(F)) is\nlarger when the probability of detection, p is lower. There are limited\nreturns from increasing the probability of detection if that probabil-\nity is already relatively high (compare larger differences between re-\nsponses for p =0.2and p =0.5to smaller differences between those\nfor p =0.5and p =0.8 in Figs. 5(B), 5(C), 5(E) and 5(F)).\n18\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\n(A) (B) (C)\n0.5 1 1.5 2\n5\n4\n3\n2\n1\n3\n4\n5\n6\n7\n8\n9\n10\n0 0.5 1 1.5 2\n4\n6\n8\n10\n0 0.5 1 1.5 20\n5\n10\n15\n(D) (E) (F)\n0.5 1 1.5 2\n5\n4\n3\n2\n1\n0\n2\n4\n6\n8\n10\n0 1 2 3 4 5\n4\n6\n8\n10\n0 1 2 3 4 50\n5\n10\n15\nFigure 5: Effectiveness of surveillance strategies in Region A (Valencia).\n(A) Mean time of detection and (D) Mean percentage of total citrus infected at the\ntime of detection. The number of host units sampled in each surveyed cell isnh =5\nand the probability of detection of symptomatic host units isp =0.5. (B,C,E,F)\nMedian and inter-quartile ranges of (B,E) time until detection and (C,F) proportion\nof citrus that is infected. The inspection interval and percentage of cells inspected\nare varied; (B,C) has fixed 5% of cells inspected at varying intervals, and (E,F)\nvaries the percentage of cells inspected at a fixed 12 month inspection interval.\nPlots show responses for three values of the probability of detection,p =0.2,0.5\nand0.8. Results are shown from ensembles of200 simulations for each set of\nparameters.\nEffectiveness of control\nDefault parameterisation\nWe examine first a single simulation using the baseline strategy (T able\n2), in which early detection surveillance is followed by more intensive\ndetection and control once the pathogen is detected (Fig. 6 and S3\nSupporting Videos (Video 3)), noting that results in this single simu-\nlation are typical of those from a much larger ensemble (see also S2\nSupporting Results, Fig. S12). Although roguing – which in this partic-\n19\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\n0\n0.2\n0.4\n0.6\n0.8\n1\n0\n0.2\n0.4\n0.6\n0.8\n1\n0\n0.2\n0.4\n0.6\n0.8\n1\n0\n0.2\n0.4\n0.6\n0.8\n1\n0\n0.2\n0.4\n0.6\n0.8\n1\n0 2 4 6 8 10 12 14 16 18 20\n0\n0.2\n0.4\n0.6\n0.8\n1\nFigure 6: Spread of the pathogen in a single simulation in Region A\n(Valencia) using baseline parameters for detection and control (T able 2).\nInitial conditions as Fig. 3. In this simulation, disease is first detected after\napproximately5 years, after which control started immediately. Maps show\ndensities of infected citrus (E +C +) in each1km × 1km cell; see also S3\nSupporting Videos (Video 3).\n20\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\nular simulation started following detection around 5 years after first\nintroduction – slows pathogen spread (compare Figs. 3 and 6), after\n20 years 65% of all citrus host units have been removed, a further\n12% of units are infected, and the epidemic is still ongoing, although\nspreading relatively slowly. Cells containing high densities of infected\ncitrus (green/yellow cells in Fig. 6(E)) are those within which commer-\ncial growers are non-compliant, and so from which no infected citrus\nis removed. Such uncontrolled locations act as a source of inoculum\ndriving the ongoing epidemic.\nSensitivity analysis\nWe do a series of one-way sensitivity scans, examining percentages\nof infected/removed citrus over time when varying single parameters\nin ensembles of simulations (Fig. 7). These scans conveniently sum-\nmarise the relative importance of different aspects of disease man-\nagement. Reducing the roguing interval (ΔR) and the compliance and\nroguing parameters ( c and q) have strong effects on the epidemic\n(Figs. 7(A), (B) and (E)), as these parameters directly impact the rate\nand/or number of units of citrus removed. Conversely, the proportion\nof cells inspected in the early detection strategy ( c) does not have\na substantial effect on epidemic rates (Fig. 7(F)), since it only affects\nthe time of first detection. Roguing commercial citrus is essential (Fig.\n7(C)), since the vast majority of citrus is commercial, although addi-\ntional management of residential/municipal citrus leads to a visible\ndifference in epidemic progression.\nHowever, the parameter with the strongest impact on control ef-\nfectiveness is m ∗, the effectiveness of additional pest management\nto reduce the size of the vector population once the pathogen is de-\ntected (Fig. 7(D)). Even before detection, we assume routine insecti-\ncide sprays lead to a m =90% reduction to vector densities in com-\nmercial citrus. However, if HLB detection triggers additional pest man-\nagement, and if the psyllid population is reduced by up to 99 %, this\n21\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\n(A) (B) (C)\n0 5 10 15 200\n20\n40\n60\n80\n100\n0 20 40 60 80 100\n0 5 10 15 200\n20\n40\n60\n80\n100\n0 20 40 60 80 100\n0 5 10 15 200\n20\n40\n60\n80\n100\n0 20 40 60 80 100\n(D) (E) (F)\n0 5 10 15 200\n20\n40\n60\n80\n100\n0 20 40 60 80 100\n0 5 10 15 200\n20\n40\n60\n80\n100\n0 20 40 60 80 100\n0 5 10 15 200\n20\n40\n60\n80\n100\n0 20 40 60 80 100\nFigure 7: Management scenarios in Region A (Valencia). Mean proportions\nof infected or removed citrus (E +C ++R) over time when varying a single\nparameter from the baseline parameterisation (Fig. 6 and T able 2). Aspects varied\nin each panel: (A) roguing interval, (B) grower compliance, (C) types of citrus\nrogued, (D) increases to the pest management parameter,m ∗, (E) roguing\nprobability, and (F) proportion of cells inspected for early detection. Inset graphs\nshow probability distributions of the proportion of infected or removed citrus after\n20 years (normalised to have the same maximum for ease of visualisation). Black\nlines show results using the baseline parameterisation; dotted lines show results\nwith no control. Averages and probability distributions calculated from ensembles\n200 simulations per parameter combination.\ncan slow the progression of the epidemic, although it does not stop\nspread completely. We return to the plausibility of such high levels of\nvector control in the EU below.\nRobustness\nWe repeat our analysis of control efficacy for Region B (Fig. 1(E)), in\nthe Andalusia region (southwestern Spain). Region B has less high-\ndensity commercial citrus than Region A, although still contains sub-\n22\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\n(A) (B) (C)\n0 5 10 15 200\n20\n40\n60\n80\n100\n0 20 40 60 80 100\n0 5 10 15 200\n20\n40\n60\n80\n100\n0 20 40 60 80 100\n0 5 10 15 200\n20\n40\n60\n80\n100\n0 20 40 60 80 100\n(D) (E) (F)\n0 5 10 15 200\n20\n40\n60\n80\n100\n0 20 40 60 80 100\n0 5 10 15 200\n20\n40\n60\n80\n100\n0 20 40 60 80 100\n0 5 10 15 200\n20\n40\n60\n80\n100\n0 20 40 60 80 100\nFigure 8: Management scenarios in Region B (Andalusia). Mean proportions\nof infected or removed citrus (E +C ++R) over time when varying a single\nparameter from the baseline case (T able 2). Individual panels as Fig. 7.\nstantial production, and more residential citrus that may hinder at-\ntempts to control spread. Region B is also much closer to where AfCP\nhas already been found, and so may be at higher risk. However since\nRegion B is further inland, there is a lower climate suitability com-\npared to Region A. Fig. 8 shows the importance of each parameter,\nequivalent to Fig. 7 for Region A (further results for Region B are in S2\nSupporting Results, Figs. S14-S18, and S3 Supporting Videos, Videos\n4-6). Impacts of control measures are remarkably similar between the\ntwo regions, and additional pest management (m ∗) remains the most\neffective intervention.\n23\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\nDiscussion\nHLB has not been reported in the EU, although invasion is possible,\nperhaps even probable (Wang, 2020). We demonstrate how mathe-\nmatical modelling can contribute to developing epidemiological pre-\nparedness for a future HLB invasion, focusing on regions in Spain con-\ntaining high-density citrus production. We found that any epidemic is\nlikely to be very well-established at the time of first detection. Even\nwith intensive disease management with almost all commercial grow-\ners participating in a large-scale programme of detection and roguing\n(i.e., removal of infected citrus trees), eradication is very likely to be\nimpossible. However, a combination of sustained and rapid disease\ncontrol via roguing and very heavy insecticide sprays may provide\nrelatively good control over sustained periods, allowing citrus produc-\ntion to be maintained for some time. This echoes the experience of\ngrowers and regulators at least some other countries, most notably\nBrazil (Bassanezi et al., 2020).\nSignificant uncertainty surrounds the invading vector and bacterium.\nAlthough our model is transferable to different vector-bacterium com-\nbinations, we focused on invasion by CLas vectored by AfCP . Of the\nthree CL species, CLas is the most widely distributed and damaging\n(Gottwald, 2010). Our choice should therefore be uncontentious. For\nthe vector, we focused on AfCP, motivated by its presence in Portugal\nand Spain, and despite recent reports of ACP from Israel (EPPO, 2022)\nand Cyprus (EPPO, 2023). Focusing on AfCP allowed us to use data\nfrom Spain and Portugal to parameterise long-range psyllid dispersal\nin our model. Although both vectors transmit CLas (Reynaud et al.,\n2022), systematic differences in CLas infection rates are not well-\ncharacterised. However, since our model explicitly includes vector cli-\nmate suitability (Fig. 1(A)), we account for AfCP’s relative lack of heat\ntolerance (Paiva et al., 2020). We used parameters and outputs from\nmodels of CLas vectored by ACP (Mastin et al., 2020; Nguyen et al.,\n2023) to parameterise short-range AfCP dispersal and HLB transmis-\n24\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\nsion rates. While this was unavoidable, given the paucity of other\ninformation, it potentially understates biological differences between\nvectors.\nUncertainty also surrounds where HLB will first enter the EU. Al-\nthough risks of entry have been modelled for the USA (Gottwald et al.,\n2019), there are no equivalent models for the EU. We therefore chose\nto focus on a reasonable worst-case scenario, with HLB introduced\ninto high-density commercial citrus in Spain, the largest EU producer\n(Schimmenti et al., 2013). We compared results for two50km ×50km\nregions, in Valencia and Andalusia (Fig. 1), and (generally) assumed\nAfCP was already locally widespread at the time of HLB invasion. Our\napproach was intended to put limits on the potential efficacy of con-\ntrol. If the vector were also actively spreading in whichever area HLB\nwas invading, as is arguably more likely, any outbreak would proceed\nslightly more slowly (Fig. 4). However, relative efficacies of different\nmanagement strategies are unaffected by prior invasion of the vector\n(S2 Supporting Results, Fig. S13).\nIn fact, while AfCP has spread widely in coastal Portugal and north-\nwestern Spain in the decade since detection (Perez-Otero et al., 2015;\nSiverio et al., 2017; Benhadi-Marín et al., 2022), it has not reached\nthe main commercial citrus areas. Furthermore, (classical) biological\ncontrol via the parasitoid Tamarixia dryi has slowed or even stopped\nspread in residential settings since 2019 (Molina et al., 2021; Duarte\net al., 2024), although how T. dryi would be affected by insecticide\nsprays in commercial citrus remains unclear. Simultaneous invasion\nof vector and pathogen has been common previously. For example, in\nCalifornia, ACP was first detected in 2008 and HLB in 2012 (Nguyen\net al., 2023), while in Florida, ACP was detected in 1998 and HLB in\n2005. However, the pathogen is harder to detect than the psyllid, and\nthere is consensus HLB was widespread in Florida by 2005 (Halbert\net al., 2010).\nThe pathogen spreads rapidly in our model following first introduc-\ntion (Fig. 3). We note a recent expert knowledge elicitation exer-\n25\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\ncise (EFSA et al., 2019a), which estimated a median spread rate of\n20.61km yr −1 (1 −99 % range 0.90 −40.12km yr −1) for HLB in the\nEU. While our spread rates are within this range, they lie towards the\nlower end, particularly early in invasions. There is a lag phase of\na few years in which spread is relatively slow (Fig. 4), particularly\nwhen the pathogen is introduced into cells with low citrus density. Of\ncourse, too, we might also note sustained spread at20km yr−1 would\nbe impossible to discern at the scale we have focused on here. By\nrestricting our attention to 50km × 50km regions, we have tended\nto de-emphasise effects of long-distance dispersal, even though this\nis included in our model, and at larger scales this would permit the\npathogen to spread even more rapidly than 40km yr −1. Given rates\nof long-distance psyllid spread in our model were calibrated to be suf-\nficient to replicate the invasion over hundreds of kilometres of coastal\nPortugal and northwestern Spain within only6 years, it is important to\nnote that impacts of HLB invasion would rapidly be realised far outside\nthe50km × 50km regions of initial invasion we focused on here.\nThe delay before first detection of HLB depends on surveillance in-\ntensity, but is 3−10 years for all parameterisations tested (Fig. 5).\nThe range is similar to, but the average again slightly lower than,\nestimates reported following the expert knowledge elicitation exer-\ncise (EFSA et al., 2019a), i.e., a median of 2.1years (1 −99 % range\n0.6−6.7years). The lower bound of3years for detection in our model\nlargely reflects the short lag before rapid spread in our model, as dis-\ncussed above. We assumed relatively large proportions of citrus were\nregularly being surveyed, and scaling this from our 50km × 50km\nregions to entire countries would be expensive. However, given we\nhad no risk of entry based reason other than high-density commercial\ncitrus to focus on the particular regions considered here, detecting\nthe pathogen within these timescales would require an equally inten-\nsive country-wide survey, at least in regions of high citrus density.\nHowever, since all three CLs are EU Priority Pests, annual surveys are\nrequired in every member state (European Union, 2016, 2019), and\n26\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\nwe note significant surveillance is currently mandated in the USA and\nBrazil (Parnell et al., 2014; Bassanezi et al., 2020). In our model, cells\nare chosen for inspection at random, weighted by citrus density. How-\never, other strategies, such as targeting locations at higher risk, may\ndetect the disease earlier or with less cost (Mastin et al., 2020; Par-\nnell et al., 2014). T esting this would be most informative if done over\nlarger spatial scales, driven by a model quantifying relative entry risks\n(Douma et al., 2016).\nWe modelled an immediate shift of strategy following detection,\nincreasing surveillance and introducing disease control region-wide.\nThe entire50km ×50km region was therefore treated as the Infested\nZone under Regulation (EU) 2016/2031 (European Union, 2016). This\nis a simplification of current plans, which are based on bounding the\ninfected area via a delimiting survey. Implementation of such surveys\nhas become increasingly statistical (EFSA et al., 2020), and is now\nbased on identifying sample sizes required for a certain confidence\nin detection given an assumed disease prevalence. Recent work has\ntested performance of strategies for Xylella fastidiosa using a (small-\nscale) individual based model (Cendoya et al., 2024). Doing this for\nHLB would be interesting, and suitable small-scale models are already\navailable (e.g., Parry et al. (2014); Craig et al. (2018)), although re-\ncalibration would be needed for use in the EU.\nRoguing does not stop the epidemic but slows spread (Fig. 6). One\ndriver is asymptomatic infection, since hosts are only removed once\nsymptoms are detectable. Another is that we assume growers do\nnot always comply with control, since HLB infected trees continue to\nproduce fruit, at least for a few years (Bassanezi et al., 2011). Fur-\nthermore, private gardens, backyard trees and abandoned orchards\nact as refugia (Cocuzza et al., 2017). During an outbreak there will be\nseveral locations where management does not occur, and these fuel\nspread. Nevertheless, even with perfect compliance by commercial\ngrowers and active management of residential citrus, transmission\nis likely to continue (Figs. 7 and 8). This is due to the cryptic pe-\n27\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\nriod within which plants are infectious but not symptomatic, and so\nnot detected/removed. Based on previous model fitting (Parry et al.,\n2014), we used a relatively lengthy asymptomatic period (1.25years\non average; T able 1). Detecting HLB before visual symptoms would\nimprove performance, even if diagnostic tests were inefficient (Mastin\net al., 2022). Impressive results have been reported from Florida us-\ning dogs trained to identify infections before symptoms are visible\n(Gottwald et al., 2020). However, transferability and application over\nlarge spatial scales remain to be tested.\nAsymptomatic infection means host removal could also be improved\nby removal of all trees within a particular radius of detected infection\n(Cunniffe et al., 2015b). This is implicitly accounted for via our host\nquantisation, since roguing removes entire commercial host units (i.e.,\nareas of100m × 100m =1 ha). However, modelling different radii of\nremoval is relatively simple (Cunniffe et al., 2016; Hyatt-T wynam et al.,\n2017), and would be an interesting extension, perhaps particularly if\ncoupled to more detailed models of grower behaviour (Murray-Watson\net al., 2023) driven by information on factors affecting stakeholder\nopinions (Garcia-Figuera et al., 2021; Exilien et al., 2024). Current\nHLB contingency plans in Portugal and Spain (DGAV, 2021; BOE, 2023)\ninclude a buffer zone surrounding the infested area within which in-\ntensive surveys and coordinated insecticide sprays should be applied.\nModelling could again be used, to optimise the size of the buffer zone\nand the type of surveillance to be applied within it, to provide quanti-\ntative support for contingency plans.\nSlowing transmission by heavily controlling vector populations with\nadditional insecticide is effective in our model (Figs. 7(D) and 8(D)), as\nit has been in Brazilian citriculture (Bassanezi et al., 2020). However,\nour model’s representation of vectors might overstate efficacy. We\ndo not model vector population dynamics, and so in turn we assume\npsyllid densities are immediately/simultaneously reduced in managed\nregions, ignoring difficulties of attaining such area-wide control (Gal-\nvañ et al., 2023). We also assume psyllid populations can be reduced\n28\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\nby up to 99% , without considering the frequency of sprays required,\nnor the expense, nor risks of insecticide resistance (which is now\nemerging in Brazil). Requisite chemical doses to achieve such reduc-\ntions seem unlikely to be consistent with EU regulations (Lázaro et al.,\n2021). While Regulation (EU) 1107/2009 does permit emergency au-\nthorisation when a pest cannot be controlled by other means (Euro-\npean Union, 2019), this applies for only a limited time. Indeed, active\ningredients currently labelled for citrus pests in the EU are less effec-\ntive than those referred to for model parameterisation; most chem-\nicals in Qureshi et al. (2014) are no longer marketed. In practice,\nit is also particularly difficult to protect flush (i.e., young) leaf tissue\nfavoured by psyllids and implicated in transmission (Cifuentes-Arenas\net al., 2018), since the most commercially attractive (i.e., cheapest)\ninsecticides are not systemic and do not cover rapidly growing tissue.\nHowever, controlling flushing frequency via selective pruning might\nprovide partial mitigation (Matias et al., 2023).\nDespite many unavoidable uncertainties, modelling provides the\nonly mechanism to understand how HLB might spread in the EU, and\nto answer questions surrounding the best approach to detect and con-\ntrol any outbreak. We conclude that the most efficient management\nstrategy would include early detection and intensive roguing to re-\nmove inoculum, alongside other measures to slow spread, particularly\nenhanced pest management to control psyllids. However, even very\neffective management will not eradicate any epidemic, and ensuring\nengagement from growers is essential. Following first detection, the\nfocus will shift to sustaining the citrus industry for the longest possible\ntime in the face of HLB (Bassanezi et al., 2020). This is another area\nin which modelling can play a prominent role.\nAcknowledgements\nThe work was supported by Pre-HLB (Preventing HLB epidemics for\nensuring citrus survival in Europe), Grant 817526 from the European\n29\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted June 6, 2024. ; https://doi.org/10.1101/2024.06.04.597414doi: bioRxiv preprint \n\nUnion Horizon 2020 program. Additionally, T.M. acknowledges support\nfrom FCT for 2020.07798.BD (doi: 10.54499/2020.07798.BD), and\nT.M and A.D. jointly acknowledge support from MED for UIDB/05183/2020\n(doi: 10.54499/UIDB/05183/2020) and from UIDP/05183/2020 (doi:\n10.54499/UIDP/05183/2020) and from CHANGE for LA/P/0121/2020\n(doi: 10.54499/LA/P/0121/2020). J.B.-M. and J.A.P . also jointly ad-\nditionally acknowledge support from FCT/MCTES (PIDDAC) for CIMO,\nUIDB/00690/2020 (doi: 10.54499/UIDB/00690/2020) and UIDP/00690/2020\n(doi: 10.54499/UIDP/00690/2020); and SusTEC, LA/P/0007/2020 (doi:\n10.54499/LA/P/0007/2020).\nCompeting interests\nNone.\nAuthor contributions\nJ.E. and N.J.C. designed the modelling framework and parameter esti-\nmation approach, and selected scenarios to test using the fitted model\nwith input from E.L., A.V. and S.P . in identifying scenarios to test. J.E.\ndeveloped and tested the computational code. E.L., B.D., T.M., A.D.,\nJ.B.-M. and J.A.P . provided or processed citrus host and/or psyllid data.\nJ.E. and N.J.C. wrote the manuscript, with input from all co-authors.\nORCID\nJohn Ellis. https://orcid.org/0000-0002-5438-4244.\nElena Lázaro. https://orcid.org/0000-0003-3821-7769.\nBeatriz Duarte. https://orcid.org/0000-0002-3373-6909.\nT omás Magalhães. https://orcid.org/0000-0002-6368-1742.\nAmílcar Duarte. https://orcid.org/0000-0002-2763-1916.\nJacinto Benhadi-Marín. https://orcid.org/0000-0002-9804-4145.\nJosé Alberto Pereira. https://orcid.org/0000-0002-2260-0600.\nAntonio Vicent. https://orcid.org/0000-0002-3848-0631.\nStephen Parnell. https://orcid.org/0000-0002-2625-4557.\nNik J. Cunniffe. https://orcid.org/0000-0002-3533-8672.\n30\n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. 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